基于板-梁理论的双轴对称三角形管翼缘工字形梁组合扭转的理论研究及有限元验证
Theoretical research and finite element verification on the torsion of biaxially symmetric triangular flange Ⅰ-shaped beam combination based on plate beam theory
张文福 1钱宏琛1
作者信息
- 1. 南京工程学院 机械工程学院,江苏 南京 211167
- 折叠
摘要
基于板-梁理论推导双轴对称三角形管翼缘工字形悬臂梁的总应变能方程,得到梁的翘曲刚度和自由扭转刚度,然后通过外力势能和总应变能得到总势能方程.再依据能量变分模型、微分方程模型及边界条件得出悬臂梁端部最大扭转角公式,将求出的最大扭转角与用ANSYS建立的有限元模型计算结果进行对比.结果表明,悬臂梁在端扭矩作用下的扭转角理论值与有限元值较为接近,误差最小的绝对值为2.40％,最大的绝对值为4.44％,可为工程设计提供参考.
Abstract
Based on the plate-beam theory,the total strain energy equation of a biaxially symmetric triangular flange I-beam is derived to obtain the buckling stiffness and free torsional stiffness of the beam,and then the total poten-tial energy equation is obtained from the external potential energy and total strain energy;The maximum torsional an-gle at the end of the cantilever beam is derived based on the energy variational model,differential equation model and boundary conditions.The calculated maximum torsion angle is compared with the results of the finite element model established by ANSYS.The results show that the theoretical value of the torsion angle of the cantilever beam under the action of end torque is close to the finite element value,with the minimum absolute value of 2.40％and the maximum absolute value of 4.44％,which can provide reference for engineering design.
关键词
板-梁理论/组合扭转/三角形截面/有限元Key words
beam/combined torsion/triangular section/plate-beam theory/finite element analysis引用本文复制引用
基金项目
国家自然科学基金面上项目(51578120)
国家自然科学基金面上项目(51178087)
国家自然科学基金(52178143)
出版年
2024
NETL
NSTL
维普
万方数据